A hybrid gradient-projection algorithm for averaged mappings in Hilbert spaces. (English) Zbl 1252.49013

Summary: It is well known that the Gradient-Projection Algorithm (GPA) is very useful in solving constrained convex minimization problems. In this paper, we combine a general iterative method with the gradient-projection algorithm to propose a hybrid gradient-projection algorithm and prove that the sequence generated by the hybrid gradient-projection algorithm converges in norm to a minimizer of constrained convex minimization problems which solves a variational inequality.


49J40 Variational inequalities
47J25 Iterative procedures involving nonlinear operators
49J45 Methods involving semicontinuity and convergence; relaxation
90C30 Nonlinear programming
74B99 Elastic materials
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